Question

how do I write a system of equations given a graph is they intercept can't be read from the graph

Answer 1

You don’t have to read the intercept from the graph to write the equation — you only need two exact points on each line (or one point plus the slope). Steps:

1. Pick two exact points on the line that fall on grid intersections (or are labeled). Call them (x1,y1) and (x2,y2).
- If you cannot find two exact points, pick one exact point and determine the slope from the grid (rise/run) or use any clearly exact point and the visible slope.
- If the line is vertical, pick an x-value (x = c) and you’re done: equation is x = c.

2. Compute the slope: m = (y2 − y1) / (x2 − x1).

3. Use point–slope form with one point: y − y1 = m(x − x1).
Then simplify to y = mx + b if you want slope-intercept form.

4. Repeat for the other line. The two resulting equations form the system.

Worked example
- Suppose one line goes through (2,1) and (5,−5). Slope m = (−5 − 1)/(5 − 2) = −6/3 = −2.
Point–slope: y − 1 = −2(x − 2) → y = −2x + 5.
- Suppose the other line goes through (1,−2) and (4,1). Slope m = (1 − (−2))/(4 − 1) = 3/3 = 1.
Point–slope: y + 2 = 1(x − 1) → y = x − 3.

System:
y = −2x + 5
y = x − 3

If the graph is faint or points are not exact, you can only write an approximate system. If you paste or upload the graph (or tell me two clear points on each line), I’ll write the exact equations for you.